to Age, and the "English Life Table" 19 



dying to the living, during an infinitely small given time dt, at 

 the precise age t years, t being either a whole number or frac- 

 tional. If a simple function of the variable t can be discovered 

 which will represent d . log e P^ at all ages, then by integration 

 the value of log e P*, and consequently of P^, may be determined 

 for all ages. It may be useful here to state that the ratio of 

 the dying to the living for an indefinitely small given time dt, 

 at the exact age t, represents the force of mortality at that age — 

 also that the vital force at any age t is represented by the reci- 

 procal of the force of mortality at the same precise point of age. 



A Table of mortality for a particular population is a mode of 

 exhibiting the ratio of the dying to the living in that population 

 for every year of age from birth-time to the end of life. The 

 knowledge of this series of annual ratios (which is the founda- 

 tion of every true Table of mortality) can be obtained only by 

 observations of the contemporary numbers living and dying at 

 every interval of age. In the making of such observations, the 

 intervals of age ought to be quinquennial at all ages above five 

 years, biennial at ages above one and less than five years, quar- 

 terly in the first year of age, and monthly in the first quarter 

 of year from birth. No observation of the kind now described 

 was known to the public until near the end of the eighteenth 

 century, when the Sweden Table of mortality constructed by 

 Dr. Richard Price was published. Dr. Halley's Table for 

 Breslau, as well as all other Tables of mortality for specific 

 populations, which had been constructed previously, were defec- 

 tive and not to be relied upon through not being founded on 

 the requisite data mentioned above. These defective Tables had 

 been deduced from observations made only on the registered 

 number of deaths at different ages belonging to the several 

 populations, without any observation or enumeration of the 

 contemporary numbers living at the same ages. The defects 

 inseparable from such Tables were partially remedied in various 

 ways. Populations were selected for observation in which the 

 numbers living at all ages were nearly stationary, and in which 

 the annual births had been nearly equal to the annual deaths for 

 a long period of time. Then the supposition was made that the 

 living population at each interval of age was constant and not 

 increased or diminished by migration. Lastly, corrections were 

 introduced to rectify manifest deviations from the assumed con- 

 dition of a stationary population at every interval of age. 



Observations made correctly, and in the proper form for de- 

 termining the vital force of man at different ages, are very few 

 in number. In the first rank are the observations of the living 

 and dying, according to age, of the population of Sweden, 

 commencing about the year 1750 and continued to the present 



C2 



